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Sorta pythagoric... (Posted on 2005-09-01) Difficulty: 3 of 5
If x, y and z are integers, 3x+4y=5z is satisfied for x=y=z=2.

Are there any other solutions?

See The Solution Submitted by e.g.    
Rating: 3.0000 (3 votes)

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Some Thoughts computer search | Comment 12 of 16 |
  5   point 20
 10   for T=0 to 1111
 20   for X=0 to T
 30    Y=T-X
 40    P=3^X+4^Y
 50    Z=log(P)/log(5)
 60    Z=int(Z+0.5)
 65    P2=int(5^Z+0.5)
 70    if P2=P then print X,Y,Z
 90   next
100   next

finds only

 0       1       1
 2       2       2

as values for x, y and z. That's checking all sets of values of x and y adding to 1111 or less.

Edited on September 2, 2005, 4:23 pm
  Posted by Charlie on 2005-09-02 16:17:57

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